Contamination from secondaries originating from interactions of
primary particles with the detector material dominates the
systematic error at low transverse momenta, but it decreases
exponentially towards higher momenta. These uncertainties are
estimated by a variation of the fit range and templates. Their values
amount to about 20% in the lowest \(p_{\rm T}\) -bin for deuterons and for
\(^{3}{\mathrm {He}}\)  in most central events. For all other centralities and
transverse momentum regions, it is significantly lower. Feed down
from weakly decaying hyper-nuclei is negligible for deuterons. The
only relevant decay of the hyper-triton,
\(^{3}_{\Lambda }{\mathrm {H}} \rightarrow \mathrm {d} + \mathrm {p} +\mathrm {\pi }^{-}\) , results in a negligible contamination, because of
the roughly 700 times smaller production cross section of the hyper-triton
with respect to the deuteron [1]}, [2]}. On the other hand, the decay
\(^{3}_{\Lambda }{\mathrm {H}} \rightarrow {\mathrm {^{3}He}} +\mathrm {\pi }^{-}\)  contaminates the \(^{3}{\mathrm {He}}\) -spectrum as these particles
are produced with similar abundance. This background is
conceptually similar to the feed down of \(\Lambda \)  decays into the
proton-spectrum [3]} though the relevant
branching ratio in the case of \(^{3}_{\Lambda }{\mathrm {H}}\) 
(25%) [4]}
is assumed
to be considerably lower than in the case of \(\Lambda \)  (64%). A detailed MC study shows
that only about 4-8% of all \(^{3}_{\Lambda }{\mathrm {H}}\)  decaying
into \(^{3}{\mathrm {He}}\)  pass the track selection criteria of primary \(^{3}{\mathrm {He}}\) .
Therefore, the remaining contamination has not been subtracted and the
uncertainty related to it was further investigated by a
variation of the DCA\(_{xy}\) -cut in data and a final error of about 5% is assigned.
Uncertainties in the material budget
have been studied by simulating events varying the amount of material by \(\pm 10\%\) . This leads to variations in the
efficiency of about 5% in the lowest \(p_{\rm T}\) -bins.
The hadronic interaction of nuclei with the detector material gives rise to an additional
uncertainty of about 6% for deuteron and for \(^{3}{\mathrm {He}}\) . The material between TPC and TOF needs
to be considered only for the deuteron spectrum above \(p_{\rm T}\)  \(>\)  1.4 GeV/\(c\)  and increases the uncertainty
by additional 7%. The corresponding corrections
for anti-nuclei are significantly larger and less precisely determined
because of the missing knowledge of the relevant elastic and inelastic
cross sections.
Details of the systematics originating from differences between the available models
are discussed in the next section.
